Baba qual quant coasts

What is a Chi-squared test used for?

A Chi-squared test is used to test objectively whether connections between variables are due to chance or whether the variables depend on one another. The result comes from comparing the observed data that has been measured with the expected data if the variable was randomly distributed.

As with all statistical techniques a hypothesis and null hypothesis are established. A hypothesis cannot be categorically proved; it can be accepted or rejected based on confidence levels.

The chi-squared equation: x² = Σ(O - E)² / E

What are the four steps of a Chi-squared test?

The process has four steps:

1. State the null hypothesis: there is no significant association between ___ and ___

2. Calculate the chi-squared figure using the equation

3. Test the significance of the result with a confidence level of 95% or 99%

4. Define the degrees of freedom (df) to use

How do you carry out a Chi-squared test? (Worked example)

An investigation into sediment size along the beach:

Hypothesis: Sediment size increases further along the beach

Null Hypothesis: There is no significant variation in sediment size along the beach

To calculate E, expected value, calculate the average (mean) for O and put the figure into the 'E' column.

Beach Site Observed Expected (O-E) (O-E)²

1 6 16 -10 100

2 9 16 -7 49

3 17 16 1 1

4 20 16 4 16

5 28 16 12 144

Total 80 310

x² = 310 / 16 = 19.38

How do you interpret Chi-squared test results?

A chi-square value on its own doesn't mean very much; it has to be tested against critical values from a published critical values table at a confidence level of 95% or 99%. This means that there is a 95% or 99% chance that the connection did not happen by chance.

The degrees of freedom is worked out very simply by taking 'n', the number of rows minus 1. In the example the degrees of freedom value is 5 - 1 = 4.

Looking at the critical values table, it is clear that the null hypothesis can be rejected at both a confidence level of 95% and 99%. This worked example, therefore, shows that there is a significant variation in sediment size along the beach.

What four things should you consider when deciding if something is significant?

When deciding if something is significant, consider four things:

· Time: How long will it take for a strategy or impact to take effect?

· Scale: How many people will be affected?

· Cost: What will the cost be? It is important to remember that just because something is expensive, that doesn't mean it is the worst option. Rather than considering whether something is expensive or cheap, think about whether it is worth the cost because of the benefits it will create

· Ethics: Does the strategy ensure dignity for local people and other stakeholders?

What is photo analysis?

This is an important observational skill. Look at the features of the foreground, midground and background. Think about what has not been included in the picture. What might be just out of frame? How do these features relate to the area studied.